Chapter A.1, Problem 31E

Solution

Simplify by removing factors from the radicand.

  $2\sqrt[4]{12}$ .

Given:

The given expression is $\sqrt{2x^3{y}^4}$ .

Concept Used:

• Find the largest factor in the radicand that is a perfect power of the index. Rewrite the radicand as a product of two factors, using that factor.
• Use the product rule to rewrite the radical as the product of two radicals.
• Simplify the root of the perfect power.

Calculation:

The given expression is $\sqrt{2x^3{y}^4}$ .

Let $a=\sqrt{2x^3{y}^4}$

  $\begin{array}{l}$ a={(2x^3{y}^4)}^{1/2}$$ a={\left(2\cdot x^2\cdot x\cdot y^2\cdot y^2\right)}^{1/2}$$ a=x\cdot y\cdot y{(2\cdot x)}^{1/2}$$ a=x{y}^2{(2x)}^{1/2}$a=x{y}^2\sqrt{2x}\end{array}$

Thus the solution of given expression $\sqrt{2x^3{y}^4}$ is $x{y}^2\sqrt{2x}$ .